To avoid civilian casualties, residents of eastern neighbourhoods of the city of Khan Younis were asked to leave the affected area, the army said.
According to eyewitness reports, thousands of people fled to supposed safe zones further west, which were already overcrowded.
Initially, there was no information about possible casualties.
An estimated 1.7 million Palestinians, around 85% of the population in the Gaza Strip, have been displaced in the wake of Israel’s offensive since October 7.
At least 37,765 Palestinians have been killed and another 86,429 injured in Gaza since then, according to the health authority in the coastal strip.
The war began after the attacks of October 7, when gunmen from Hamas and other militants killed more than 1,200 people in southern Israeli communities.
Around 20 rockets had been fired at Israel from Gaza on Monday, the Israeli army said.
The missile defence system intercepted some, others hit the open ground.
Hamas said it had fired the rockets.
There were no casualties, the Israeli army said.
There was an air alert in towns near the border with the Gaza Strip and people had to rush to shelters.
The army once again accused Hamas of systematically violating international law and using civilian infrastructure as cover for weapons.
The army repeatedly reports that there are rocket launching pads in residential areas, weapons depots in schools and tunnels for fighters under hospitals.
Israeli ground troops continue to be deployed with support from the air in Shejaiya.
Shejaiya is a residential area in the east of Gaza City, as well as in the centre of the strip and south in the city of Rafah.
